Four poplars

Four poplars are growing along the way. The distances between them are 35 m, 14 m, and 91 m. At least how many poplars need to be dropped to create the same spacing between the trees? How many meters will it be?

Result

n =  16
x =  7 m

Solution:

35=57 14=27 91=713 GCD(35,14,91)=7  x=GCD(35,14,91)=7 m s=35+14+91=140 m n=s/x4=140/74=1635=5 \cdot 7 \ \\ 14=2 \cdot 7 \ \\ 91=7 \cdot 13 \ \\ \text{GCD}(35, 14, 91)=7 \ \\ \ \\ x=GCD(35,14,91)=7 \ \text{m} \ \\ s=35+14 + 91=140 \ \text{m} \ \\ n=s/x -4=140/7 -4=16
x=7 mx=7 \ \text{m}



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